Why Is 254 Used in the Braking Distance Formula?

[hugo_faurand]

Hello everyone !
I'm working on my highway code and my book give me the approximate formula and the real formula of the braking distance. Here's the real formula according to the book :

$$ Bd = \frac{V^2}{254 \times f} $$

With :
V : the velocity
f : the adherence coefficient.

But I have on question. Where does this 254 come from ?

Thanks in advance.
Regards

Hugo

 

[Doc Al]

That factor is a units conversion when V is measured in km/h instead of the usual m/s.

 

[hugo_faurand]

That factor is a units conversion when V is measured in km/h instead of the usual m/s.

It's strange, usually we multiply (or divide) by 3.6 when we want to convert m/s in km/h (km/h in m/s).

 

[Doc Al]

It's strange, usually we multiply (or divide) by 3.6 when we want to convert m/s in km/h (km/h in m/s).

Right. That 254 is more than just a units conversion, it also contains part of the standard formula: $$\frac{V^2}{2 g \times f}$$

 

[hugo_faurand]

Right. That 254 is more than just a units conversion, it also contains part of the standard formula: $$\frac{V^2}{2 g \times f}$$

Sorry but I don't find the right calculus. 2*9.8 = 19.6 So I don't understand how you find this 254.

 

[Doc Al]

Sorry but I don't find the right calculus. 2*9.8 = 19.6 So I don't understand how you find this 254.

2*9.8 takes care of the 2g factor. Now include the conversion from (km/h)^2 to (m/s)^2. That requires multiplying by (1/3.6)^2, which gives you a constant of 2*9.8*3.6^2 = 254 in the denominator.

 

[hugo_faurand]

2*9.8 takes care of the 2g factor. Now include the conversion from (km/h)^2 to (m/s)^2. That requires multiplying by (1/3.6)^2, which gives you a constant of 2*9.8*3.6^2 = 254 in the denominator.

AH I see. Highway code should tells us the unit of V. Thank you ! :)

 

[Rim23]

Great answer. I have also been wondering where the 254 comes from. Now its easier to remember which speed to convert with 3.6 or 0.27778 and which speed does not require conversion because the factor is alredy included in either 254 or 3.6 or 0.694 (TeV). Thank you.